由计算得:x^3+y^3=a^3-3/2*(a^2-b)*a
#include "stdio.h"
void main()
{
int a,b;
while(scanf("%d%d",&a,&b)!=EOF)
{
printf("%d\n",a*a*a-(a*a-b)*a*3/2);
}
}
公式推导:
x+y=a
x^2+y^2=b
上式平方-下式:
2xy=a^2-b
xy=(a^2-b)/2
公式:x^3+y^3=(x+y)(x^2-xy+y^2)
=a(b-(a^2-b)/2)
=ab-a^3/2+ab/2
=3ab/2-a^3/2
=a(3b-a^2)/2
#include "stdio.h"
void main()
{
float a,b;
scanf("%f%f",&a,&b);
printf("已知 x+y=a=%f,x^2+y^2=b=%f, 求得x^3+y^3 =%f\n",a,b,a*(3.0*b-a*a)/2.0);
getchar();getchar();
}